Finite element modelling of bridging micro-mechanics in through-thickness reinforced composite laminates

Abstract

Delamination and debonding are the major failure modes in laminated composites, which significantly reduce the performance of a structure under compressive or bending loads. To overcome this problem, new composites with through-thickness reinforcement (TTR) have been used to improve the interlaminar strength and damage tolerance of laminated composites [Freitas G, Fusco T, Campbell T, Harris J, Rosenberg S. Z-fiber TM technology and products for enhancing composite design. In: 83rd Meeting of AGARD SMP, 1996, CP-590; Farley GL, Dickinson LC. Mechanical response of composite materials with through-the-thickness reinforcement. NASA CR-14753, 1993. p. 123–43; Cartié DDR, Partridge IK. Delamination behaviour of Z-pinned laminates In: Williams JG, Pavan A. editors, Proceedings of second ESIS TC4 conference, Les Diablerets, Switzerland, 13–15 September 1999, ESIS Publication, 2000. ISBN 008 043710-9; Greenhalgh E, Hiley M. The assessment of novel materials and processes for the impact tolerant design of stiffened composite aerospace structures. Comp Part A: Appl Sci Manuf 2003;34(2):151–61. [1–4]]. Although the TTR can change the structural elastic response of a composite laminate [Stringer LG, Hiley MJ. Through-thickness reinforcement of composites: Z-pinning, Stitching, and 3D weaving. In: 14th International conference for composite materials, ICCM14, 11–14 July, San Diego, CA, 2003; Mouritz AP, Leong KH, Herszberg I. A review of the effect of stitching on the in-plane mechanical properties of fibre-reinforced polymer composites. Composites Part A 1999;28A:979–91; Grassi M, Zhang X, Meo M. Prediction of stiffness and stresses in z-fibre reinforced composite laminates. Comp Part A: Appl Sci Manuf 2002;33(12):1653–64; Patridge IK, Cartié DDR, Troulis M, grassi, M, Zhang X. Evaluating the mechanical effectiveness of Z-pinning. In: Proceedings of SAMPE/Dayton technical conference, 2003. [5–8]] they start working only when delamination propagates in their field, which provides non-linear bridging closure forces that shield the delamination crack from the full delaminating force and moment of the applied loads [Grassi M, Zhang X. Finite element analyses of mode I interlaminar delamination in z-fibre reinforced composite laminates. Comp Sci Technol 2003;63(12):1815–32; Robinson P, Das S. Mode I DCB testing of composite laminates reinforced with z-direction pins: a simple model for the investigation of data reduction strategies. Eng Fract Mech 2004;71(3):345–64. [9,10]]. Fiber pull-out test has been developed in order to study the micro-mechanics of the TTR bridging a crack under Mode I loading conditions [Cartié DDR, Cox BN, Fleck NA. Mechanisms of crack bridging by composite and metallic rods. Comp Part A: Appl Sci Manuf 2004;35(11):1325–36. [11]], and several analytical models have been developed to analyze these phenomena [Cox B. A constitutive model for through-thickness reinforcement bridging a delamination crack. Adv Comp Lett 1999;8(5):249–56; Jain LK, Mai YW. On the effect of the stitching on Mode I delamination toughness of laminated composites. Comp Sci Technol 1994;51:331–45; Allegri G, Xiang Z. Private communications, 2004. [12–14]]. In terms of energy the TTR fiber pull-out can be accompanied by significant amount of energy dissipation due to the frictional work at interface; this process absorbs part of the energy that would otherwise be placed at the delamination front of the structure. The basic objective of this research project was to develop an efficient and accurate finite-element-based numerical tool to simulate the spontaneous propagation of a single TTR pull-out under quasi-static conditions and in the presence of frictional contact between the fiber/matrix interface. The pull-out phenomenon was studied assuming a constant friction coefficient at the interface along the TTR axial direction and using improved contact-elements to solve the frictional contact problem. Load/displacement bridging curves of the fiber pull-out process, which includes elastic deformation with a fully/partially bonded interface plus frictional sliding, were calculated. Moreover, the effect of friction model was also investigated. Numerical results were validated by experimental observations of debonding and frictional sliding of a fiber in steady-state pull-out tests under pure Mode I loading conditions.